Compared to stationary formats, “flow-through” polymerase chain reaction (PCR) offers advantages in terms of speed, sample throughput, ease of thermal control and integration with other microfluidic operations. However, current flow-through PCR approaches that are based on continuous flow of reactants in fixed channels lack flexibility because the available thermal profiles are determined by the physical layout of the channels. There is a need for droplet-based approaches to flow-through PCR.